If the vertex angle of an isosceles triangle measures 99°, what are the measures of the base angles?

Explanation

We will use the fact that the base angles of an isosceles triangle have the same measure and the sum of the angle measures of any triangle is 180° to write an equation that mathematically models the situation.  We can then solve the equation to find the unknown angle measures.

The base angles of an isosceles triangle have the same measure. If we let represent the measure of one base angle, the measure of the other base angle is also . (See the figure to the right.) Since the sum of the measures of the angles of any triangle is 180°, the sum of the measures of the base angles and of the vertex angle is 180°.We can use this fact to form an equation.

\[x + x + 99^o = 180^o\]

• Combine like terms: x + x = 2x
  • \(2x + 99^o = 180^o\)
• To isolate the variable term, ex, undo the addition of 99° from both sides
  • \(2x = 81^o\)
• To isolate x, undo the multiplication by 2 by dividing both sides by 2
  • \(\frac{2x}{\color{red}{2}} = \frac{81^o}{\color{red}{2}}\)
• \(x = 4.5^o\)

The measure of each base angle is 40.5°.